Denarians, as we know, can implant a "shadow" of themselves within the mind of a mortal who knowingly/intentionally handles a coin.
It doesn't appear to be like a magical "tag," where touching an unwilling or unknowing subject gives that person a Shadow. You gotta know what you're doing, and do it either intentionally or carelessly. Similarly, merely "handling" a coin isn't sufficient to release the Fallen and become their host. You must, it seems, agree to that role; you must "make a deal with the Devil," so to speak.
Still, there is that "Shadowed" step, between being host to one of the Fallen and being utterly free of the coin & its Fallen.
But thanks to @morriswalters, I just realized something...
In Proven Guilty, Michael Carpenter tells Harry how to eliminate the shadow:
“Give up the coin of your own will. And set aside your power. If you do, Lasciel’s shadow will dwindle with it and waste away.”
Hmm. That's how a WIZARD can do it. (How can a MUGGLE do it? Or CAN they even? More on that below...).
Then we look at Harry's magic. Even before the Shadow manifested to Harry, in dream or illusion, it was still giving Hellfire to Harry's magic; mostly to Fuego, but also to Forzare. Simply running his will through his staff (to get the runes glowing) brought a hint of brimstone.
Taken together, it appears that a Denarian Shadow -- in a wizard -- links directly and to their
magic, not merely to their "mind."
I mean, yeah there's stuff like the "eidetic memory" trick, gift-of-Tongues, etc. Mental tricks that aren't explicitly "magical."
But the Shadow was affecting Harry's spells
without him understanding how, or what to do about it; and the Church knows that setting aside magic will cause a Shadow to "whither" alongside the magic.
So the
Shadow -- in a Wizard -- is linked
specifically to their
magic!
Other mortals (from above), non-wizards? How do they get free? I'm going to go over to Father Forthill's wisdom in Proven Guilty:
“Power,” he said, waving a hand in an all-encompassing gesture. "Magic. Physical strength. Economic strength. Political strength. It all serves a single purpose..."
So I'll venture a WAG that any Muggle would set aside the Shadow by setting aside their mundane strength. Retire from politics (including all consulting, being interviewed, writing op-ed pieces, lobbying, etc); give away all their wealth; etc. Someone with physical strength would be particularly challenged, I think; they'd have to set up their life to operate as if they were of average-or-less strength, and intentionally act within those limits. Take more trips carrying smaller loads, pack smaller bags/boxes to carry, etc.